Pfaffian solutions to a (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation and its modified counterpart

A class of exact Pfaffian solutions to a (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation is obtained. A set of sufficient conditions consisting of systems of linear partial differential equations involving free parameters is generated to guarantee that the Pfaffian solves the equation. A Bäcklund transformation of the equation is presented. The equation is transformed into a set of bilinear equations, and a few classes of traveling wave solutions, rational solutions and Pfaffian solutions to the extended bilinear equations are furnished. Examples of the Pfaffian solutions are explicitly computed, and a few solutions are plotted.